Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719625 |
| Sylow | C13 ⋊ C2×#568 |
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #16785349, #16785359, #16785379, … |
| maximal normal subgroup of | #16785349, #16785359, #16785379, … |
| maximal quotient of | C2×#13131402, C2×#13131408, C4×#11719625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21504);